Adjoint node-based shape optimization of free-floating vessels

• DOI: 10.1007/s00158-022-03338-2
• Publication Date: 2022-08-23T09:03:05Z
• Authors: Niklas Kühl; Thanh Tung Nguyen; Michael Palm; Dirk Jürgens; Thomas Rung
• Keywords: Froude number

Abstract The paper is concerned with a node-based, gradient-driven, continuous adjoint two-phase flow procedure to optimize the shapes of free-floating vessels and discusses three topics. First, we aim convey that elements Cahn–Hilliard formulation should augment frequently employed Volume-of-Fluid model maintain dual consistency. It seen such consistency serves as basis for robust primal/adjoint coupling in practical applications at huge Reynolds Froude numbers. second topic covers different strategies. A central aspect application floating position, particularly trim sinkage, interact variation hydrodynamic loads induced by shape updates. Other topics addressed refer required level density more straightforward—yet non-frozen—adjoint treatment turbulence. third part computation descent direction within node-based environment. We will illustrate means deform both volume mesh hull simultaneously same time obey technical constraints on vessel’s displacement its extensions. Hilbert-space approach provides smooth updates using established coding infrastructure computational fluid dynamics algorithm access managing additional constraints. Verification validation follow from submerged 2D cylinder case. includes full-scale offshore supply vessel $$\mathrm{Re} = 3 \times 10^8$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Re</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>8</mml:mn> </mml:msup> </mml:mrow> </mml:math> $$\mathrm{Fn} 0.37$$ <mml:mi>Fn</mml:mi> <mml:mn>0.37</mml:mn> . Results fully parallel can automatically reduce drag an already pre-optimized 9–13% $$\approx\,{\mathcal{O}}$$ <mml:mo>≈</mml:mo> <mml:mspace /> <mml:mi>O</mml:mi> (10,000-30,000) CPUh depending considered couplings floatation aspects.